The Fire Crystal to Crescent Island

After you collect the crystal pieces, go see Cid on the steamship.   He will run off to Karnak.  When you see him on the 2nd floor of the inn, he will tell your party to go away.  Apparently he thinks that the crystals shattering is all his fault.  The townspeople say his son, Mid, is at the Ancient Library.   Maybe he can help.
	Leave Karnak and go west, then south, until you reach the Ancient Library.
The scholars at the Library tell you that Mid went to go look for a particular book in the basement, which is full of monsters!
	After filling up on HP and MP with the recovery pot, go into the basement.   Some of the bookshelves seem to be haunted!  Get them to move out of your way (There are particular places you must stand), until you reach the one that tells you it won't let you pass.  If you go out of the room, you'll see a ladder going up into the books.  Its a secret passage.  Go up the ladder, tap the A button, and a passage will appear that leads to Ifrit.
While fighting Ifrit, be sure to keep everyone's HP up.  His Fire2 spell is devastating, and his High Kick attack will paralyze whoever it hits.  Have whoever has Black Magic ability repeatedly hit him with Ice2.  Be sure not to let a character's HP fall too low, he tends to target those near death.
	After you defeat Ifrit, you will be able to use him as a Call beast!   Go back to the bookshelf, and Ifrit will scare him out of the way.
Save on the savepoint, and go forward.  There's Mid, but he doesn't seem to see you.  Byblos does though.
	While fighting Byblos, have your Caller and Black Wizard (or people with those skills) blast him with Ifrit and Fire2, and have your Time Wizard cast Slow on Byblos and Fast on all your party members.  He casts Safe on himself early on, so physical attacks will do little.  Be sure to recover quickly from his Gale Cut, two of those in a row will finish you.
It looks like Mid has been reading a book the whole time!  He even knows a secret exit!  Follow him back into the main part of the library.
	In the library, Mid tells everyone that he found a book that will allow him and Cid to get the steamship working again!  He hurries off to tell Cid.
Go back to Karnak and see Cid.  Mid will show up and beat some sense into Cid.  Cid says the last crystal, the Earth Crystal, must be protected.  With that he and and Mid go off to repair the steamship.
	Go to the steamship.  While Cid and Mid repair it, Galuf has a flashback!  He remembers that he is from another world, and he came to prevent the return Exdeath, and evil being from another world.  He and 3 others sealed Exdeath here 30 years ago.
After he and Mid repair the steamship, go to Crescent island.  It is far to the east (use the map you found in the Ship Graveyard.)  Cid also tells you that if you ever get into any trouble, to just go back to the Ancient Library.